11520

# Comparing Two Means Using Independent Samples of Unknown Variance

This Demonstration illustrates the hypotheses testing of the means of two independent populations with unknown variances, based on independent samples. These are the parameters used in this example:
(unknown) mean of the first population
(unknown) mean of the second population
hypothesized difference between the two population means
level of significance
size of the first sample
size of the second sample
mean of the first sample
mean of the second sample
standard deviation of the first sample
standard deviation of the second sample
You can alter all of these parameters, except for the population means that are being tested, using the provided sliders. Using the tabs, you can also test all three types of hypotheses (right-tailed, left-tailed and two-tailed) and assume that the unknown population variances are unequal or equal. This Demonstration dynamically shows the results of the hypothesis testing, with the red vertical line representing the calculated -value, and the area in the appropriate tail representing the -value. The black line represents the critical value, and the associated area in the appropriate tail is the level of significance. If the calculated value is more extreme (further along the appropriate tail) than the critical value, the conclusion of "reject " is provided at the top of the graph (otherwise, if the calculated value is more toward the center compared to the critical value, the text "fail to reject " appears).

### DETAILS

Reference
[1] A. H. Kvanli, R. J. Pavur and K. B. Keeling, Business Statistics: Analytics for Decision Making, Stamford, CT: Cengage Learning, 2010.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.